Molecular beam epitaxial growth of III-V semiconductor ... - KOBRA

More documents

Recommendations

Info

Theoretical Background of Semiconductor Nanostructures Structure Degree of connement Dimension of the structure Bulk 0 3D Quantum well (QW) 1 2D Quantum wire (QWR) 2 1D Quantum dot (QD) 3 0D Table 2.1: Classication of semiconductor nanostructures and their degree of quantum connement. According to Eq. 2.1 if one-dimension of a bulk semiconductor (assuming, box geometry) (L x , L y , L z ) is in the order of the de-Broglie wavelength (λ B ) or smaller (Eq. 2.2), the quantum size eect gets signicant. The wave-like behavior of electrons are also important on much longer dimensions, if you have to care on coherent phenomena. This is also true for band-structure formation caused by the coherent interaction with the periodic potential of the lattice and is valid in the whole solid. You would not understand this without using quantum mechanics [19]. L x , L y , L z ≤ λ B (2.2) 2.3.1 Density of States Function of Low-Dimensional Systems In quantum physics, the electronic structure is often analyzed in terms of the density of electron states (DOS). The DOS function, at a given value E of energy, is dened such that g(E)∆E is equal to the number of states (i.e. solutions of Schrödinger equation) in the interval energy ∆E around E. However, if the dimensions L i (i = x, y, z) are macroscopic and if proper boundary conditions are chosen, the energy levels can be treated as quasi-continuous [19]. On the other hand, in the case where any of the dimensions L i gets small enough, the DOS function becomes discontinuous. Fig. 2.2 describes how the density of states changes as a function of dimensionality. It is clear that the density of state function (DOS) in Fig. 2.2 gets sharper as the dimension of the structure becomes 14
2.3 Low-Dimensional Semiconductor (Nanostrtuctures) Figure 2.2: The density of state functions (DOS) of semiconductor with dierent degrees of freedom 3, 2, 1 and 0 of electron propagation, the system with 2, 1 and 0 degrees of freedom referred as quantum wells, quantum wires and quantum dots respectively. Figure modied according to reference [21]. smaller, which is a potential advantage for the electronic and optical properties. The density of state function (DOS) for dierent semiconductor structures shown in Fig. 2.2 are mathematically expressed as: g(E) 3D = 1 3 2π 2 (2m∗ ) 2 √ E (2.3) 2 g(E) 2D = m∗ ∑ σ(E − E π 2 n ) (2.4) g(E) 1D = 1 π ∑ √ n n m ∗ 2(E − E n ) σ(E − E n) (2.5) g(E) 0D = ∑ n 2δ(E − E n ) (2.6) Where m ∗ is the eective mass and E n are the energies of the quantized states inside the nanostructure, σ(E − E n ) is the step function, and δ(E − E n ) is the Dirac delta function [21]. However, in quantum dots (QDs) the energy level are 15
Page 1: Molecular Beam Epitaxial Growth of
Page 4 and 5: Gutachter (Supervisors): 1. Prof. D
Page 6 and 7: patterns indicating a 2D smooth sur
Page 8 and 9: (MEE = migration enhance epitaxy) u
Page 10 and 11: viii
Page 12 and 13: CONTENTS 3.4.4 Planar Defects Assoc
Page 14 and 15: CONTENTS xii
Page 16 and 17: Introduction thesis a detailed stud
Page 18 and 19: Introduction 1.1.2 Thesis Approach
Page 20 and 21: Introduction 1.2 Thesis Outline The
Page 22 and 23: Theoretical Background of Semicondu
Page 36 and 37: Heteroepitaxial Growth of III-V Sem
Page 64 and 65: Experimental Growth and Characteriz
Page 78 and 79:
MBE Growth of Self-Assembled InAs a
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
MBE Growth of InAs and InGaAs Quant
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Optimization of MEE and MBE growth
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
Conclusions substrates, respectivel
Page 144 and 145:
REFERENCES [8] J. M. Gerard, O. Cab
Page 146 and 147:
REFERENCES [29] http://www.wmi.badw
Page 148 and 149:
REFERENCES [49] M. R. Brenner: GaP/
Page 150 and 151:
REFERENCES [66] Y. Ishida, T. Takah
Page 152 and 153:
REFERENCES [84] A. Garcia, C. M. Ma
Page 154 and 155:
REFERENCES [100] M. Felici, P. Gall
Page 156 and 157:
REFERENCES [116] H. Usui, H. Yasuda
Page 158 and 159:
REFERENCES [133] Grassman, T. J. Br
Page 160 and 161:
Conferences Contributions: Tariq Al
Page 162 and 163:
Nomenclature
Page 164 and 165:
REFERENCES symbol Descriptions γ f
Page 166 and 167:
like to thank all member of the Ins
Page 168:
REFERENCES Erklärung Hiermit versi
show all

Molecular beam epitaxial growth of III-V semiconductor ... - KOBRA

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?